The N-point DFT of a sequence x[n], 0 ≤ n ≤ N - 1 is given by
$$X\left[ K \right] = \frac{1}{{\sqrt N }}\sum\limits_{n = 0}^{N - 1} {x\left[ n \right]} {e^{ - j\frac{{2\pi }}{N}nK}},0 \leqslant K \leqslant N - 1$$
Denote this relation as X = DFT(x). For N = 4, which one of the following sequences satisfies DFT (DFT (x)) = x.

The Fourier transform of a real valued time signal has

The RMS value of a rectangular wave of period T, having a value of +V for a duration, T₁(< T) and -V for the duration, T - T₁ = T₂ equals

A continuous time function x(t) is periodic with period T. The function is sampled uniformly with a sampling period T_s. In which one of the following cases is the sampled signal periodic?

The phase response of a passband waveform at the receiver is given by
$$\varphi \left( f \right) = - 2\pi \alpha \left( {f - {f_c}} \right) - 2\alpha \beta {f_c},$$
where f_c is the centre frequency, and α and β are positive constants. The actual signal propagation delay from the transmittance to receiver is